A group action on increasing sequences of set-indexed Brownian motions
Probability
2015-08-13 v1
Abstract
We prove that a square-integrable set-indexed stochastic process is a set-indexed Brownian motion if and only if its projection on all the strictly increasing continuous sequences are one-parameter -time-changed Brownian motions. In addition, we study the "sequence-independent variation" property for group stationary-increment stochastic processes in general and for a set-indexed Brownian motion in particular. We present some applications.
Keywords
Cite
@article{arxiv.1508.02858,
title = {A group action on increasing sequences of set-indexed Brownian motions},
author = {Arthur Yosef},
journal= {arXiv preprint arXiv:1508.02858},
year = {2015}
}
Comments
Published at http://dx.doi.org/10.15559/15-VMSTA31 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/). arXiv admin note: text overlap with arXiv:1009.5748 by other authors